Trimetallic CoMo3W9/Al2O3 catalyst is prepared using the Keggin structure mixed heteropolyacid H4SiMo3W9O40 and cobalt citrate. CoMo12/Al2O3 and CoW12/Al2O3 catalysts based on H4SiMo12O40 and H4SiW12O40, respectively, are synthesized as reference samples. Sulfided catalysts are analyzed by high-resolution transmission electron microscopy and X-ray photoelectron spectroscopy. Catalytic properties are investigated in the co-hydrotreatment of dibenzothiophene (DBT) and naphthalene in a flow unit. It is shown that the catalytic activity in both DBT hydrodesulfurization and naphthalene hydrogenation (HYD) decreases in the following sequence: CoMo12/Al2O3 > CoMo3W9/Al2O3 > CoW12/Al2O3, and it correlates with the degree of promotion of active-phase particles by cobalt atoms. A comparison with the published data available for Ni-promoted catalysts makes it possible to reveal the general regularity for bi- and trimetallic Со(Ni)-Mo(W)S catalysts: the use of mixed Mo-W H4SiMo3W9O40 heteropolyacid instead of monometallic H4SiW12O40 causes an increase in the degree of promotion of MoWS2 crystallite edges for the series of catalysts promoted by both cobalt and nickel. The use of nickel as a promoter leads to a higher degree of promotion of edges of active-phase particles in comparison with cobalt; as a result, the NiMo3W9/Al2O3 catalyst is much more active than the CoMo3W9/Al2O3 counterpart. Possible reasons behind the found features are discussed.